论文信息 - Contracting an element from a cocircuit

Contracting an element from a cocircuit

We consider the situation that M and N are 3-connected matroids such that |E(N)|>=4 and C^* is a cocircuit of M with the property that M/x"0 has an N-minor for some x"[email protected]?C^*. We show that either there is an element [email protected]?C^* such that si(M/x) or co(si(M/x)) is 3-connected with an N-minor, or there is a four-element fan of M that contains two elements of C^* and an element x such that si(M/x) is 3-connected with an N-minor.

Dillon Mayhew | Rhiannon Hall | Rhiannon Hall | Dillon Mayhew

[1] James G. Oxley,et al. Matroid theory , 1992 .

[2] Charles Semple,et al. Generalized Delta?-Y Exchange and k-Regular Matroids , 2000, J. Comb. Theory, Ser. B.

[3] Bert Gerards,et al. The Excluded Minors for GF(4)-Representable Matroids , 1997, J. Comb. Theory, Ser. B.

[4] Paul Seymour,et al. Triples in Matroid Circuits , 1986, Eur. J. Comb..

[5] C. Semple,et al. Generalized ? Y Exchange and K{regular Matroids , 1998 .

[6] Paul D. Seymour,et al. Decomposition of regular matroids , 1980, J. Comb. Theory, Ser. B.

[7] R. Bixby. A simple theorem on 3-connectivity , 1982 .

[8] Xiangqian Zhou,et al. A Splitter Theorem for Internally 4-Connected Binary Matroids , 2006, SIAM J. Discret. Math..

[9] Charles Semple,et al. The structure of the 3-separations of 3-connected matroids , 2004, J. Comb. Theory, Ser. B.

[10] Manoel Lemos. On 3-connected matroids , 1989, Discret. Math..

[11] Rhiannon Hall. On contracting hyperplane elements from a 3-connected matroid , 2009, Adv. Appl. Math..

[12] M. Lemons. On 3-connected matroids , 1989 .

[13] Charles Semple,et al. Maintaining 3-connectivity relative to a fixed basis , 2008, Adv. Appl. Math..

[14] Charles Semple,et al. The structure of equivalent 3-separations in a 3-connected matroid , 2005, Adv. Appl. Math..